Ocean-driven thinning enhances iceberg calving andretreat of Antarctic ice shelvesYan Liua,b, John C. Moorea,b,c,d,1, Xiao Chenga,b,1, Rupert M. Gladstonee,f, Jeremy N. Bassisg, Hongxing Liuh,Jiahong Weni, and Fengming Huia,b

aState Key Laboratory of Remote Sensing Science, College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China;bJoint Center for Global Change Studies, Beijing 100875, China; cArctic Centre, University of Lapland, 96100 Rovaniemi, Finland; dDepartment of EarthSciences, Uppsala University, Uppsala 75236, Sweden; eAntarctic Climate and Ecosystems Cooperative Research Centre, University of Tasmania, Hobart,Tasmania, Australia; fVersuchsanstalt für Wasserbau, Hydrologie und Glaziologie, Eidgenössische Technische Hochschule Zürich, 8093 Zurich, Switzerland;gDepartment of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, MI 48109-2143; hDepartment of Geography, McMickenCollege of Arts & Sciences, University of Cincinnati, OH 45221-0131; and iDepartment of Geography, Shanghai Normal University, Shanghai 200234, China

Edited by Anny Cazenave, Centre National d’Etudes Spatiales, Toulouse, France, and approved February 10, 2015 (received for review August 7, 2014)

Iceberg calving from all Antarctic ice shelves has never beendirectly measured, despite playing a crucial role in ice sheet massbalance. Rapid changes to iceberg calving naturally arise from thesporadic detachment of large tabular bergs but can also betriggered by climate forcing. Here we provide a direct empiricalestimate of mass loss due to iceberg calving and melting fromAntarctic ice shelves. We find that between 2005 and 2011, thetotal mass loss due to iceberg calving of 755 ± 24 gigatonnes peryear (Gt/y) is only half the total loss due to basal melt of 1516 ±106 Gt/y. However, we observe widespread retreat of ice shelvesthat are currently thinning. Net mass loss due to iceberg calvingfor these ice shelves (302 ± 27 Gt/y) is comparable in magnitude tonet mass loss due to basal melt (312 ± 14 Gt/y). Moreover, we findthat iceberg calving from these decaying ice shelves is dominatedby frequent calving events, which are distinct from the less fre-quent detachment of isolated tabular icebergs associated with iceshelves in neutral or positive mass balance regimes. Our resultssuggest that thinning associated with ocean-driven increasedbasal melt can trigger increased iceberg calving, implying that ice-berg calving may play an overlooked role in the demise of shrink-ing ice shelves, and is more sensitive to ocean forcing thanexpected from steady state calving estimates.

iceberg calving | basal melt | mass balance | ice shelf | Antarctica

The majority of Antarctica’s mass loss to the ocean occursthrough its fringing ice shelves via iceberg calving and basal

melt (1–3). Although the mass balance of ice shelves has a neg-ligible direct effect on sea level rise (because the ice shelves floatfreely), the ice shelves buttress the grounded ice upstream andhave been shown to play a major role in stabilizing the dischargeof grounded ice to the ocean (4–6). Reduction of buttressing dueto increased iceberg calving or basal melt leads to thinning andacceleration of inland glaciers (4–7), and may be driven by re-gional and global changes in atmospheric and oceanic conditionsthrough ice−ocean and ice−atmosphere interactions (4, 5, 7–11).Catastrophic ice shelf disintegration driven by atmosphericwarming has led to abrupt ice shelf retreat in the Antarctic Pen-insula (5, 11), which, combined with basal melt induced thinning,has contributed to the 34% increased discharge of grounded ice tothe ocean from West Antarctica from 1996 to 2006 (6).The mass balance of an ice shelf is determined by the differ-

ence between mass gained from the flux of ice across thegrounding line into the ice shelf, deposition of snow on thesurface or marine ice on the bottom of the ice shelf, and masslost by melting (surface and basal) and iceberg calving. In steadystate, the ice shelf has no areal extent change (steady-statecalving front) and no thickness change (steady-state ice thick-ness). It is possible to define a steady-state basal melt (or marineice accretion) necessary to maintain steady-state ice thickness forgiven cross-grounding line fluxes, surface mass balance, andcalving fluxes (2). Similarly, the steady-state iceberg calving is

defined as the calving flux necessary to maintain a steady-statecalving front for a given set of ice thicknesses and velocities alongthe ice front gate (2, 3). Estimating the mass balance of iceshelves out of steady state, however, requires additional in-formation about the change of ice thickness and the change ofareal extent of the ice shelf, which is determined by the advanceor retreat of the calving front. Several recent studies have soughtto estimate the nonsteady-state mass balance of ice shelves atbroad scales (2, 3, 12), but these studies indirectly inferred ice-berg calving assuming a steady-state calving front, neglecting thecontribution of advance or retreat of the calving front to the massbalance of ice shelves (2, 3). Such “flux gate” calculations are in-evitably biased, as they underestimate iceberg calving for retreatingice shelves or overestimate it for advancing ice shelves. This de-ficiency is problematic not only for estimates of the mass balance ofice shelves but also because current models of iceberg calvingprovide conflicting predictions about whether increased basal meltwill lead to an increase or decrease in iceberg calving (1, 13–15).Here we avoid the assumption of steady-state calving front by

combining traditional estimates of ice shelf mass balance with anannual record of iceberg calving events larger than 1 km2 from allAntarctic ice shelves exceeding 10 km2 in area for the period2005–2011. Our observations show that both iceberg calving(Fig. 1) and ice shelf extent (Fig. 2) change over the observationalperiod, proving that the steady-state calving front assumption isinvalid. To estimate mass loss due to iceberg calving, we manually

Significance

The floating parts of the Antarctic ice sheet (“ice shelves”) helpto hold back the flow of the grounded parts, determining thecontribution to global sea level rise. Using satellite images, wemeasured, for the first time, all icebergs larger than 1 km2

calving from the entire Antarctic coastline, and the state ofhealth of all the ice shelves. Some large ice shelves are growingwhile many smaller ice shelves are shrinking. We find highrates of iceberg calving from Antarctic ice shelves that areundergoing basal melt-induced thinning, which suggests thefate of ice shelves may be more sensitive to ocean forcing thanpreviously thought.

Author contributions: Y.L., J.C.M., and X.C. designed research; Y.L. and F.H. performedresearch; Y.L., J.C.M., X.C., R.M.G., J.N.B., H.L., J.W., and F.H. contributed new reagents/analytic tools; Y.L., J.C.M., X.C., R.M.G., J.N.B., H.L., J.W., and F.H. analyzed data; and Y.L.,J.C.M., X.C., R.M.G., J.N.B., H.L., and J.W. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1To whom correspondence may be addressed. Email: xcheng@bnu.edu.cn or john.moore.bnu@gmail.com.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1415137112/-/DCSupplemental.

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delineated annual cumulative area calved based on Envisat Ad-vanced Synthetic Aperture Radar (ASAR) images from theAugusts of 2005, 2006, 2007, 2008, 2009, 2010, and 2011 with vi-sual interpretation and spatial adjustment, in combination withestimates of the average ice thickness of the calved regions fromIce Cloud and Land Elevation Satellite (ICESat) and IceBridgedata (Materials and Methods and SI Materials and Methods).In addition to annual mass loss due to iceberg calving, obser-

vations of surface features on images and recurrence interval ofcalving provide additional qualitative information about the styleof calving (SI Discussion). For example, we observe isolated tabular

bergs that detach along the boundary of isolated preexisting frac-tures visible in a time series of satellite images (Fig. 3A). Theseevents are thought to be part of the natural cycle of advance andretreat of ice shelves and are sufficiently infrequent that observa-tional records spanning many decades would be needed to de-termine nonsteady-state behavior (13, 16–18). In contrast, we alsoidentify more frequent sequences of smaller-scale calving events(typically much less than 100 km2). These disintegration events aresometimes preceded by the formation of melt ponds on the surfaceof the ice shelf, suggesting hydrofracture-driven disintegration,as occurred for the Larsen B Ice Shelf (Fig. 3B) (5, 8, 19).

Fig. 1. Spatial distributions of basal melt and iceberg calving. The area of the red circles denotes mass loss due to iceberg calving of 26 basin systems. Thedashed lines divide the ocean around Antarctica into five regions: Weddell Sea (60°W–20°E), Indian Ocean (20°E–90°E), Western Pacific Ocean (90°E–160°E),Ross Sea (160°E–130°W), and Bellingshausen/Amundsen Sea (130°W–60°W). Abbreviations of subbasin systems are described in Dataset S1.

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Surprisingly, other disintegration events that we observe occurredin colder environments with little or no evidence for surface melt.These events typically occurred in regions with large-scale visiblerift and crevasse zones and a rapidly flowing ice front (Fig. 3C) andare difficult to detect because the readvance of the ice front par-tially obscures the change in calving front position.In conjunction with quantifying iceberg calving, we also de-

veloped a flow-line method to quantify cross-grounding linefluxes for the whole of Antarctica (Materials and Methods). Usingthese techniques, we provide an estimate of Antarctic ice shelfmass balance that is not constrained by the steady-state as-sumption. The mass balance of ice shelves is presented both interms of volumetric components (net ice shelf volume change

due to thickness and extent changes) and its budget components(surface mass balance, cross-grounding line fluxes, iceberg calv-ing, and basal melt). Moreover, steady-state iceberg calving andsteady-state basal melt are also estimated and agree well withprevious estimates (2, 3) (Tables S1 and S2). We calculated allthese components and associated uncertainties for 7 large drain-age systems (Filchner-Ronne, East Antarctica KB, Amery, EastAntarctica CE, Ross, West Antarctica, and Peninsula), 26 basinsystems labeled A∼K’, and 94 subbasin systems covering theentire continent (Fig. 1 and Dataset S1).We find that the mean annual mass balance of all Antarctic ice

shelves is slightly positive (46 ± 41 Gt/y) between 2005 and 2011,but with large interannual variability because of the irregular

Fig. 2. Antarctic ice shelf advance and retreat be-tween 2005 and 2011. (A) Larsen B and C Ice Shelf;(B) Fimbulisen, Jelbartisen, and Ekströmisen Ice Shelf;(C) Amery Ice Shelf; (D) Totten and Moscow UniversityIce Shelf; (E) Mertz Glacier Tongue; (F) Ross Ice Shelf;(G) Getz Ice Shelf; and (H) the floating parts of PineIsland and Thwaites Glaciers, and Crosson Ice Shelf.

Fig. 3. Different calving features. (A) Example oftabular calving from the Fimbulisen Ice Shelf, (B) ex-ample of melt pond induced disintegration from theLarsen B ice shelf, and (C) example of crevasse induceddisintegration from the Totten glacier. (1) Calving fea-ture on synthetic aperture radar image in 1997 (brightwhite ponds shown in B image are melt ponds).ENVISAT ASAR image with area calved marked before(2) and after (3) calving. (4) Ice front changes overlaidon Envisat ASAR image in 2011.

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occurrence of extralarge-size (larger than 1,000 km2) calvingevents (Table 1 and Fig. 4A). Our calculated basal melt of 1516 ±106 Gt/y accounts for two thirds of Antarctic ice shelf total massloss while iceberg calving of 755 ± 25 Gt/y accounts for theremaining third (Table 1). The total contribution of icebergcalving to the mass balance might be much higher if the recordsof infrequent large iceberg detachment are extended by severaldecades. For example, a sequence of major calving events such asthose that detached from the Amery Ice Shelf in 1963–1964 (17)or from the Ross and Filchner-Ronne Ice Shelf in 2001–2002(20), would result in a (temporary) net negative mass balance forAntarctic ice shelves. We detect 579 distinct iceberg calvingevents, ranging in size from 1 km2 to 3,115 km2 over the 7-y studyperiod. As we have data at monthly resolution for only 3 y (15),the calving events we detect may have resulted from eithera sequence of several separate calving events or a single largercalving event. Only three cases larger than 1,000 km2 aredetected: the calving of the Mertz Ice Tongue by iceberg colli-sion (21); the calving of the floating part of Thwaites Glacier byprogressive rifting (10); and the disintegration of the Wilkins IceShelf, possibly caused by ocean-driven basal melt (19). However,95% of calving events are small and medium in scale (1∼100 km2

in size), accounting for about 38% of total calving mass over the7-y study (Tables S3 and S4).In contrast with recent studies suggesting most ice shelves are

close to steady state (3), our basal melt and iceberg calvingresults (Table 1 and Fig. 4B) indicate significant mass imbalancein more than three quarters of ice shelf subbasin systems. Wefind two opposing regimes or patterns of mass loss aroundAntarctica. There are 43 ice shelf subbasin systems in positivemass balance, and, for these ice shelves, basal melt and calvingare just 74% (P < 0.1 in Student’s t test) and 13% (P < 0.001),respectively, of their inferred steady-state values (Table 1 andFig. 4C). Most calving events on these ice shelves produce in-frequent, isolated tabular icebergs (Fig. 3A and Fig. S1) and donot reoccur at the same location during our observation period(1997−2011). This previously documented tabular calving style isthought to be primarily controlled by internal stress and char-acterized by a natural cycle with several decades of quiescencebetween major calving events (13, 16–18).There are 33 ice shelf subbasin systems in negative mass bal-

ance, but they account for only about 18% of total ice shelf area.These subbasins account for 73% of the total mass loss, com-prising 67% of total Antarctic ice shelf basal meltwater pro-duction (1018 ± 90 Gt/y) and 85% of total calving (641 ± 43Gt/y). For these ice shelves, basal melt and calving are 144%

(P < 0.01) and 189% (P < 0.01), respectively, of their steady-state values. Twenty-four of these subbasins experienced both iceshelf retreat and thinning (Dataset S1). We note that the “in-creased” basal melt we report is referenced relative to ourinferred steady-state basal melt and hence, by definition, leads toice shelf thinning. Similarly, the enhanced iceberg calving is alsorelative to the steady-state calving required to maintain a con-stant calving front position and hence “enhanced” calving leadsto ice shelf retreat and area loss. Thus, the negative mass balanceof these ice shelves results not only from increased basal melt (2,3, 12) but also from increased iceberg calving. Contributions tothe net mass loss from ice shelf thinning and calving front retreatare similar (Table 1). This is true even for the floating parts ofPine Island and Thwaites Glaciers, which are among the best-studied on the continent (22). Both of these ice tongues calvedlarge (larger than 500 km2) tabular icebergs twice between 1997and 2011. However, they experienced more frequent sequencesof smaller-scale calving events, typically of less than 100 km2

(Fig. S1 and Table S3). This mode of calving, associated withrapid-flowing ice fronts and intense crevassing and rifting (e.g.,Fig. 3C), is common to many of the retreating ice shelves we

Table 1. Mean mass balance of Antarctic ice shelves in different state during 2005–2011

Components

State of ice shelf mass balance

Negative Near-zero Positive Total

Number of subbasin systems 33 17 43 93*Total ice shelf area, km2 284,292 98,522 1,159,293 1,542,108Ice shelf mass balance, Gt/y −614 ± 34 4 ± 6 655 ± 37 46 ± 41Volumetric components, Gt/y

Mass change due to thickness change −312 ± 14 −20 ± 5 107 ± 25 −226 ± 25Mass change due to extent change −302 ± 27 24 ± 3 549 ± 27 271 ± 21

Budget components, Gt/yGrounding line flux 929 ± 60 203 ± 10 838 ± 41 1970 ± 75Surface mass balance 116 ± 9 30 ± 2 200 ± 9 346 ± 37Steady-state basal melt 706 ± 92 180 ± 13 405 ± 63 1290 ± 110Basal melt 1018 ± 90 200 ± 12 298 ± 58 1516 ± 106Steady-state iceberg calving 339 ± 30 53 ± 4 633 ± 29 1026 ± 39Iceberg calving 641 ± 24 29 ± 3 84 ± 7 755 ± 25

*One of the 94 subbasin systems has no ice shelf larger than 10 km2.

Fig. 4. Annual Antarctic iceberg calving from 2005 to 2011. (A) All ice shelves bycalving size; (B) calving by state of mass balance; (C) ice shelves in positive massbalance; and (D) ice shelves in negativemass balance. Horizontal lines in B, C, andD denote steady-state iceberg calving for those ice shelves.

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observed. These frequent calving events have been overlookedby previous studies, which assumed that calving is dominated byinfrequent tabular berg calving. The calving front retreat asso-ciated with ice shelves in negative mass balance has a robustlyidentifiable trend over our study period (Fig. 4D) due to theshorter recurrence intervals typical of these more frequentlycalving systems. However, calving (and basal melting) may alsovary over decadal and longer time scales not captured by ourlimited observational period.The ice shelves undergoing calving front advance and/or ice

thickening are the large ice shelf drainage systems (Filchner-Ronne,Ross, and Amery Ice Shelf) together with the neighboring systemsof I”J, D’E, and KA’, in the Ross Sea, Weddell Sea, and IndianOcean regions (Fig. 2). These ice shelves account for 78% of theentire Antarctic ice shelf area. They have a positive or near-zeromass balance and are located at high southern latitudes or are fedby an ice sheet grounded well above sea level. These regions areboth cold and continental in character and have low net snow ac-cumulation. For some sections of these ice shelves, basal freezingoccurs (Fig. 2), which often coincides with observed marine ice“stripes” (23). Marine ice is softer than meteoric ice and has beenhypothesized to play an important role in filling and healing bottomcrevassing along shear zones, hence determining ice shelf durability(and length of calving cycles) (24–26).The ice shelves in negative mass balance are primarily small to

medium ice shelves located around the Antarctic Peninsula (H’I’)and West Antarctica in the Bellingshausen/Amundsen Seas, andEast Antarctica along the Wilkes Land coastline (C’D) (Fig. 2, Fig.S1, Dataset S1, and Table S3). The ice shelves in negative massbalance of the Antarctic Peninsula are fed locally, have smallgrounding line fluxes, and have thinner than average ice fronts (Fig.2 and Dataset S1). The presence of surface meltwater ponds due torising atmospheric temperatures has led to catastrophic disintegra-tion events (8, 27), which have only occurred, to date, on theAntarctic Peninsula (24). However, basal melt much larger thannecessary to maintain a steady-state ice thickness may have alsocontributed to the demise of Antarctic Peninsula ice shelves. Forexample, basal melt exceeded ice flux across the grounding lineafter 2005 for the more southerly locatedWilkins Ice Shelf (DatasetS1), suggesting that it experienced high ocean-driven thinning be-fore disintegration. The southern edge of George VI Ice Shelf isalso experiencing increased basal melt and is undergoing similar,but localized, disintegration (7). Increased basal melt driven bywarmer water masses beneath the shelves could also diminish oreven halt marine ice formation within suture zones that occur incolder ocean environments, reducing the stabilizing effect on basalfractures, and ice shelf structural integrity (25, 26, 28).The ice shelves in negative mass balance of the West Antarctic

systems F’H’ and East Antarctic systems CD’ are mostly fed bymarine based glaciers grounded well below sea level. The rapidresponse time of these high-throughput systems, which experi-ence high surface accumulation and basal melt (3), may be fur-ther increased by the marine ice sheet instability (1) andassociated feedbacks. This results in small and potentially vul-nerable ice shelves. The presence of both ice shelf thinning andretreat in this region (Dataset S1) hint at a connection betweenincreased basal melt and enhanced iceberg calving. Warm Cir-cumpolar Deep Water (CDW), or slightly modified CDW, liesjust off the continental shelf break in these regions (29). Thomaet al. (30) postulated that wind-driven increases in upwellingdrive CDW over the continental shelf break and into ice shelfcavities, increasing basal melt and leading to the pronouncedobserved ice shelf thinning (11, 30, 31). While the relationshipbetween increased basal melt and ocean forcing is clear, it is lessclear whether the observed enhanced iceberg calving is simplya direct result of ice shelf thinning or is driven by more complexsubshelf processes. It is possible that pronounced and spatiallyvarying basal melt can undercut the submerged ice fronts (9).

Additionally, increased melting of ice mélange, a mixture of seaice, snow, ice shelf fragments, and marine ice trapped in betweenthe rifts may accelerate rift propagation and threaten ice shelfstability (32, 33). Large-scale crevasse-like surface features arecommon on the ice shelves along F’H and CD’. Recent obser-vations from ground-penetrating radar show that many of theseare, in fact, the surface expression of deep and wide transversebasal crevasses (13, 34) or longitudinal subglacial melt channels(35). The basal channels or crevasses can be incised 200 m intothe ice shelf base (34, 35), and the surface depressions can bemore than 30 m lower than the usual ice shelf surface (36),making the features the thinnest regions of the ice shelves. Thesecrevasse-like features may provide multiple sites for potentialfull-thickness crevassing and rift opening. Models show that thetensile stress induced by these wide basal channels is sufficient tocause additional surface and basal crevasse propagation (34, 35).Increased basal melt may enhance this process, as the thinnershelf will flex more and increase the likelihood of full-thicknessrift formation (35). For example, Totten Glacier is an ice shelfthat has experienced thinning due to increased basal melt, andwe observe calving associated with surface troughs (Fig. 3C).These crevasse-like zones cover a considerable area of iceshelves in the F’H’ and CD’ regions, potentially rendering manyAntarctic ice shelves susceptible to massive, catastrophic dis-integrations in the event of further increases in basal melt (15).Given these results, we propose that ocean-driven increased

basal melt enhances fracturing of Antarctic ice shelves. We alsosuggest that the numerous small ice shelves along the AntarcticPeninsula, Amundsen Sea Embayment, and Wilkes Land thathave experienced marked increases in basal melt and icebergcalving over the past 2 decades may be poised for major retreat.This needs to be better understood so that it can be factored intofuture sea level projections.

Materials and MethodsThe mass change of an ice shelf, ΔM, over a given time period, Δt, calculatedin terms of volumetric components as the sum of change due to mean shelfthickness change, ΔMH (negative for thinning), and change due to arealextent change (i.e., advance/retreat of ice front), ΔMA (negative for retreat),is approximately given by a Taylor Series,

ΔM=ΔMH +ΔMA =A0ΔHρi +H0ΔAρi [1]

where ρi is the ice density, A0 and ΔA are the reference area and change inarea, H0 and ΔH are the reference mean ice thickness and change in meanice thickness, and we have neglected higher-order terms in the expansion.The reference values are based on the mean values from the 2005–2011period. We combined the ice shelf area changes of Antarctic ice shelves in2005–2011 with 2003–2011 ice thickness and 2003–2008 ice shelf thicknesschanges to estimate the Antarctic ice shelf mass balance. Ice shelf extentchanges are identified by coregistered pairs of monthly ASAR data forAugust 2005 and August 2011. Ice thicknesses are estimated by combiningthe direct measurements in 2009–2011 from Multichannel Coherent RadarDepth Sounder (MCORDS) by Operation IceBridge mission with the indirectestimates in 2003–2009 from the Geoscience Laser Altimeter System (GLAS)instrument aboard ICESat (SI Materials and Methods). Average ice shelfthickness change for the period 2003–2008 is derived by the procedure inref. 12 using ICESat-1 GLAS data.

The mass balance can also be expressed in terms of budget componentsin Gt/y.

ΔMΔt

= FG + SMB−C −B [2]

where FG is the integrated flux into the ice shelf across the grounding line(calculated using flux gates; see SI Materials and Methods), C is the rate ofchange of mass due to iceberg calving, SMB is the surface mass balance (thedifference between surface accumulation and ablation rate), and B is therate of change of mass due to basal melt (negative for freeze-on).

Cross-Grounding Line Flux. We use the Interferometric Synthetic ApertureRadar (InSAR) velocities and ice thicknesses at the flux gates to calculate

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cross-grounding line flux FG. Ice thicknesses are estimated by combiningMCORDS data and ICESat GLAS data (SI Materials and Methods). Flux gatesare positioned at the grounding line as determined by a combination of twopublished data sets. For the most part, the more accurate InSAR groundingline position is used, but where coverage is lacking, the grounding line fromimagery and ICESat GLAS is used to achieve complete coverage. Cross-grounding line flux is determined using a flow-line routing algorithm (SIMaterials and Methods, Figs. S2 and S3). Ice fluxes are estimated by ice flowacross each unit of 900-m-width pixel at the grounding line. More than20,000 flux units around Antarctica are calculated.

Surface Mass Balance.We use the surface mass balance product derived froma firn model UUFIRNMODELv3.1/ANT forced by climate data from RACMOv3.2/ANT27 for the period 2003–2008 (12).

Iceberg Calving. Iceberg calving is the actual rate of ice mass loss due toiceberg calving rather than a “flux gate” calculation (2, 3). It is calculated asthe product of the mean ice thickness of the area loss due to calving andarea of annual calving losses (SI Materials and Methods). The area enclosedbetween the outer boundary (ice shelf front) and the inner boundary(fracture line) over the annual interval gives the calving area. Calving areasare manually traced from coregistered pairs of consecutive August 2005–2011 Envisat ASAR image mosaics with a spatial resolution of 75 m andgeolocation accuracy of 50 m (SI Data). Because ice shelves move forward,calving area detection requires tracing both ice shelf margin (ice front) andthe fracture line in the original image (before calving) and the second image(after calving). The ice front is delineated by an automated object-orientedclassification method based on watershed segmentation combined withmanual modifications (Fig. S4 A and B). Identifying the fracture line is donemanually with visual interpretation and spatial adjustment. In the case oftabular calving (Fig. 3A), calving area at the ice shelf front is obviously visi-ble; in the case of calving associated with large-scale crevassing (Fig. 3C),surface features at the ice front of the second image can be matched withfeatures in the original image, allowing the fracture line to be estimated(Fig. S4 C and D); in the other case of calving (e.g., Fig. 3B) where featurescannot be uniquely identified, advance of the starting ice front is estimatedby a flow-line method (SI Materials and Methods).

Basal Melt. An estimate for B is obtained by rearranging Eq. 2.

B= FG + SMB−C −ΔMΔt

: [3]

Steady-State Iceberg Calving. The steady-state iceberg calving, assuming nochange of ice shelf areal extent, is the sum of iceberg calving and masschange rate due to extent change (positive for advance and negativefor retreat).

Css =C +ΔMA

Δt[4]

Steady-State Basal Melt. The steady-state basal melt, assuming no change ofice shelf thickness, is calculated as the sum of basal melt and mass changerate due to ice thickness change (positive for ice thickening and negativefor ice thinning).

Bss =B+ΔMH

Δt: [5]

ACKNOWLEDGMENTS. We thank M. R. van den Broeke and S. R. M. Ligtenbergfor providing firn depth correction data, European Space Agency for providingEnvisat ASAR data, and National Snow and Ice Data Center for distribution ofother data. We thank the editor, two anonymous reviewers, T. A. Scambos, andK. C. Wang, whose comments substantially improved the manuscript. We alsothank H. Huang, X. Li, F. Wang, T. Ci, T. Zhao, and M. Zhai for assistance withdata processing. This research is supported by Chinese Arctic and AntarcticAdministration, National Basic Research Program of China Grants 2012CB957704and 2015CB953600; National Natural Science Foundation of China, Grants41406211, 41176163, 41106157, and 41276188; National High-tech R&D Pro-gram of China Grants 2008AA121702 and 2008AA09Z117; Chinese PolarEnvironment Comprehensive Investigation & Assessment Programmes; Fun-damental Research Funds for the Central Universities of China; and YoungTalent fund of the State Key Laboratory of Remote Sensing Science. R.M.G. isfunded by Marie Curie Actions within the European Commission FrameworkProgramme 7, and J.N.B. was supported by National Science FoundationGrants NSF-ANT 114085 and NSF-ARC 1064535.

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3268 | www.pnas.org/cgi/doi/10.1073/pnas.1415137112 Liu et al.

Supporting InformationLiu et al. 10.1073/pnas.1415137112SI DiscussionCharacteristics of Antarctic Iceberg Calving.Spatial distribution of iceberg calving in different styles. Previousobservations of surface features on images have documented twostyles of iceberg calving: “tabular” calving (1–4) and “dis-integrating” calving (3, 5–7). The infrequent repeat interval ofour imagery precludes us from determining if the disintegrationevents we detect initiated as a single tabular berg that dis-integrated after detaching or as a sequence of individual bergsthat detached from the calving front along preexisting crevasses.Moreover, because large tabular events detach infrequently, ourobservations provide little information about whether ice shelvesthat predominantly experienced disintegration style events dur-ing our observation period are more or less prone to tabular bergdetachment. Nonetheless, because smaller-scale disintegrationevents occur frequently, our observations do inform about theabsence of disintegration events from ice shelves. Thus, we userecurrence interval (Iceberg calving) to classify our observedevents into infrequent and frequent calving, which may thenindicate tabular or disintegration styles.Identification of the recurrence of a calving event requires that

the recurred event happens in the same spatial neighborhood asthe first, and that the two events are of the same order ofmagnitude. By this definition, only 152 of the 579 calving eventsdid not recur in the period of 1997–2011. Surface features suggestthat these events are tabular berg detachment. In this paper,we thus classify them as infrequent “tabular” calving eventand classify the other 427 events as frequent “disintegration”calving events.Fig. S1 and Table S3 show the spatial distribution of the 579

iceberg calving events occurred in Antarctica from 2005 to 2011.Frequent disintegration calving dominates in the Peninsula, WestAntarctica, and the East Antarctica CE sectors, which also havethe largest number of calving events. For example, Totten Glacier(sector CE) and Wilkins Ice Shelf (Peninsula) calve nearly everyyear. In contrast, infrequent tabular calving dominates the EastAntarctica KB, Ross, and Amery sectors. No calving event wasobserved in the Filcher-Ronne sector.Spatial scale features of Antarctic iceberg calving. Mean percentage ofcalving events, area, and mass loss binned into four differentspatial scale categories from 2005 to 2011 are shown in Table S4.Frequency increases as calving area decreases, but there is arelatively small increase at the smallest scales. By contrast, meanannual calving area and mass loss in the medium, large, and extra-large calving scales are similar, and sum to more than 93% of thetotal. The calving events of less than 100 km2, which were oftenignored in previous studies, accounted for 95% of the meanannual number of events, 32% of the area loss, and 38% of massloss. However, the smallest size scale (less than 10 km2) con-tributes less than 7% of total mass loss. This suggests that ob-servations of smaller calving events will only slightly improve theaccuracy of our estimate but add significant workload. Thus, thespatial resolution of ASAR data satisfies the needs for calvingarea detection (see also SI Data).

Characteristics of Antarctic Ice Shelf Mass Balance. The detailed re-sults of Antarctic ice shelf mass balance and its componentsare shown in Dataset S1.

Comparison with Other Studies.Comparison of area delineation. A previous estimate of total area ofAntarctic ice shelves is 1,561 million km2, reflecting ice front

location in 2007–2008 (8), whereas our 1,542 million km2 showsthe average over 2005–2011 (Dataset S1).Comparison of cross-grounding line flux.We use the methods of least-squares estimate (LSE) and York’s linear regression with errors(9) to compare our estimated ice flux to previous results (10).This shows that there is good consistency between these twodifferent methods (R > 0.9). We expect the two results to bedifferent because earlier work (10) did not include about 20% ofthe total Antarctic grounding line (GL), while we make use ofour flow-line routing algorithm to calculate the whole GL flux.Comparison of steady-state calving flux.Table S1 shows that our resultis slightly lower than found by earlier studies (8). However, theprevious methods are susceptible to overestimation of ice front fluxgate lengths if the shape of ice shelf margins is complex, especiallywhere the presence of rifts complicates the geometry. Even con-sidering the angle between flow direction and ice front line cannotcompletely remove the effect of overlapping flux gates.Comparison of basal melt.Area mean basal melt rates in meters peryear from our study, and the glaciological estimate (8), the Finite-Element Sea-Ice Ocean Model (FESOM) model (11), and theBremerhaven Regional Ice Ocean Simulations (BRIOS) model(12) are compiled in Table S2. Melt rates from this study areconsistent with the glaciological estimate (8), except for meltunder the Filchner-Ronne Ice Shelf mainly due to the quitedifferent thickening rates of the shelf. We use the same sourcefor ice shelf change rates as ref. 8, but our study shows a massgain from ice shelf thickening of 73 ± 18 Gt/y, in accordance withthe ice shelf thickening rate of 0.02 ± 0.005 m/y (13), while ref. 8shows mass loss from ice shelf thinning of 61 ± 18 Gt/y. Apossible explanation for the difference may be that ref. 8 as-sumes steady state.

SI DataWe use multisource satellite data, updated remote sensing-basedproducts, and model products to quantitatively estimate geo-metric and flux components of Antarctic ice shelf mass balance.The key parameters are calculated with data that have lowuncertainties and high time consistence. These data include re-mote sensing images, surface elevation, ice thickness, surface iceflow velocity, GL, ice thickness, geoid model for geoid correctionof surface elevation, firn depth correction (FDC) for ice thicknesscalculation, and land cover map. We also used published data,including surface mass balance and ice thickness change ofAntarctic ice shelves.The data sets used to calculate ice shelf mass balance and its

volumetric and budget components in this study can be found atthe following websites: bprc.osu.edu/rsl/radarsat/data/ [RAMPAMM-1 SAR Image Mosaic of Antarctica (14)], nsidc.org/data/nsidc-0280 [MODIS Mosaic of Antarctica (MOA) (15)], earth.esa.int[European Space Agency (ESA) Environmental Satellite (Envisat)ASAR Wide-Swath Mode (WSM) image (2005−2011)], nsidc.org/data/docs/daac/glas_icesat_l1_l2_global_altimetry.gd.html [GLAS/ICESat L1 and L2 Global Altimetry Data, Version 33 (16)],nsidc.org/data/irmcr2 [IceBridgeMultichannel Coherent RadarDepth Sounder (MCORDS) L2 Ice Thickness (17)], www.antarctica.ac.uk//bas_research/our_research/az/bedmap2 [Bedmap 2 (18)],nsidc.org/data/docs/measures/nsidc0484_rignot/ [MEaSUREsInSAR-Based Antarctica Ice Velocity Map (19)], nsidc.org/data/docs/measures/nsidc0498_rignot/ [MEaSUREs Antarctic GroundingLine from Differential Satellite Radar Interferometry (DInSAR)(20)], nsidc.org/data/docs/agdc/nsidc0489_bindschadler/ [ASAIDHigh-resolution Image-derived Grounding and Hydrostatic Lines

Liu et al. www.pnas.org/cgi/content/short/1415137112 1 of 10

for the Antarctic Ice Sheet (21)], icgem.gfz-potsdam.de/ICGEM/[EIGEN-6C2 Geoid (22)], and doi.pangaea.de/10.1594/PANGAEA.775983 [Surface mass balance (SMB) (13), 2003–2008].Envisat is an advanced polar-orbiting Earth observation satellite

that was launched in March 2002 by ESA. It carries sophisticatedoptical and radar instruments, and Advanced Synthetic ApertureRadar (ASAR) is the largest single instrument. WSM is oneof the five operating modes of ASAR. Envisat ASAR WSM(henceforth simply ASAR) data use the ScanSAR techniquewith a swath of 405 km and spatial resolution of 150 m, andprovides HH (horizontal transmitting, horizontal receiving)and VV (vertical transmitting, vertical receiving) polarizationimages, and measures radar backscatter strength of C-band8,000–4,000 MHz (3.8–7.5 cm). Its nominal resolution (pixelsize) is 75 m. Generally, it only takes 3 d to cover all Antarcticcoastline. ASAR Level 1B product ASA_WSM_1P N1 filesare used in this study. Together with precise orbit data fromDOR_VOR_AXVF files (available at https://earth.esa.int/), theyare geolocated and resampled onto the projected grid based onpolar stereographic projection. The geolocation accuracy andprecision are tested by a thorough comparison with the RAMPAMM-1 image with an estimated geolocation accuracy of 50 m(23). It showed that the accuracy of geolocation data are betterthan 75 m (a pixel size). The mosaic ASAR images of Augusteach year in 2005–2011, which repeatedly covered the Antarcticcoastline, are used to monitor annual calving events and ice frontadvance and retreat.The observations of iceberg calving events of Antarctic ice shelves

for the period 2005–2011 are available online at www.nature.com/ngeo/journal/v7/n12/full/ngeo2290.html#supplementary-information(Supplementary Data) and are described in the Calving EventCatalogue (nature.com/ngeo/journal/v7/n12/extref/ngeo2290-s6.pdf).

SI Materials and MethodsIce Shelf Mass Balance Estimation.Antarctic surface flow line mapping.The discharge to the Antarctic iceshelves is routed through widespread complex flow in the interiorof the Antarctic ice sheet. Surface flow lines (also termed“streamlines”) are delineated either by flow directions calculatedfrom Digital Elevation Model (DEM) or by flow features on sat-ellite images usually only distributed in fast flow area that are lim-ited in their potential to track the flow from ice divide to ice shelffront. We propose a method that automatically assesses the startingpositions and the whole route of an ice flow line on the surface onlybased on the horizontal flow direction calculated from the surfacevelocity map for the period 2007–2008 (Ice flow velocity). In a rastermap of flow direction, flow direction is the attribute of a grid celland grid direction is an approximation to ice flow direction, limitedby the restriction that flow lines must pass through cell centers. Thedirection searching accuracy is defined as the difference betweenflow direction and grid direction. Lookup tables between flowdirections and grid directions of different direction searching ac-curacy are set to adapt to the actual flow direction accuracy of thedata, which varies spatially. The highest searching accuracy is upto 0.1 degree. The principle of no crossing between flow lines isused to estimate the actual direction accuracy, which is typicallybetween 0.5 degrees and 5 degrees.We use this method to track the full range of high-density

surface flow lines of Antarctica (Fig. S2), giving the most detailedview of the complex Antarctic flow system to date. The flow lineshave a very good agreement withmost surface longitudinal featureson satellite images. The flow line map shows ice shelf ice origins,flow trajectories and regions of convergence or confluence.Delineation of Antarctic ice sheet drainage−ice shelf systems. The def-inition of ice sheet drainage−ice shelf system is an importantprocess when developing estimates both of ice sheet and ice shelfmass balance. A principle aim of this study is to develop esti-mates of ice shelf mass balance and their relationship with ice

sheet mass balance using common divides. The previous detaileddefinition of Antarctic ice sheet drainage divides are based onICESat DEM at 500 m resolution and include 26 distinct basins(10, 24) and 65 drainage subbasins (10) [note that about 1/5 ofAntarctic ice is not included within the survey (24)], assigned intothree major components of East Antarctica, West Antarctica, andthe Peninsula. In contrast, here we include all of the subbasins. Wealso separate the ice sheet into seven major sectors identified by therouting of ice to major ice shelves (Fig. 1). We delineated drainagedivides based on ref. 10, but we added the fringing floating partsdelineated by the ice flow-line routing algorithm (Fig. S2).In this study, Antarctic ice sheet drainage−ice shelf system is

divided into 7 sectors, 26 basin systems, and 94 subbasin systems.The seven sectors include the Filcher-Ronne Ice Shelf system(Filchner-Ronne), East Antarctica KB system (East AntarcticaKB), Amery Ice Shelf system (Amery), East Antarctica CB sys-tem (East Antarctica CE), Ross Ice Shelf system (Ross), WestAntarctica F’H system (West Antarctica), and Antarctic Penin-sula system (Peninsula) (Fig. S1). Every sector has several basinsystems labeled A to K’. Ninety-four individual subsystems aregrouped into large units (Fig. 1 and Dataset S1).Delineation of ice shelf extent.The area between the GL and ice frontexcluding ice rises and islands is defined as ice shelf extent. All ofthe ice shelves larger than 10 km2 are included in this paper(Dataset S1). Differential Interferometric Synthetic ApertureRadar (DInSAR) derived Antarctic GL in 1994–2009 [one datasetof the NASA Making Earth System Data Records for Use inResearch Environments (MEaSUREs), available at nsidc.org/data/docs/measures/nsidc0498_rignot/] (19, 20), complementedwith visible imagery in 1999–2003 and laser altimetry in 2003–2009derived Antarctic GL [one dataset of the Antarctic Surface Ac-cumulation and Ice Discharge (ASAID) project, available at nsidc.org/data/docs/agdc/nsidc0489_bindschadler/) (21), are selected. Icefront coastlines are identified in two mosaics of monthly ASARdata for August 2005 and August 2011, respectively. The thoroughcomparison with the first Antarctic Mapping Mission (AMM-1)synthetic aperture radar images of the Canadian RADARSAT-1/2satellites (RADARSAT-1/2 images) and coastlines (14, 25) are usedto test the consistency and quality. The ice fronts delineated fromASAR data have a good agreement with RADARSAT-1/2 ice frontin ice front areas with little or no change. Averages of ice shelf areain 2005 and 2011 are used in estimation of volume ice shelf thickeningor thinning (Ice shelf thickening or thinning) and area mean basalmelt rates (Basal melt).Ice thicknesses.We calculate thicknesses at GLs and ice shelf frontsfor estimating GL fluxes, iceberg calving rates, and mass gain (orloss) from advance (or retreat). Ice thickness is calculated usingdirect measurements of actual thickness from the NASA IceBridgeMission (IceBridge) MCORDS and indirect estimates from ICESatGeoscience Laser Altimeter System (GLAS) derived ice shelfsurface elevation assuming hydrostatic equilibrium. The data areavailable at the National Snow and Ice Data Center (NSIDC)(nsidc.org/data/icebridge/data_summaries.html and nsidc.org/data/icesat/data.html). Ice thicknesses from Bedmap2 (18) are used forno-data areas and consideration of marine ice under ice shelves(available at antarctica.ac.uk//bas_research/data/access/bedmap/).

Individual thickness calculation.The actual thickness of an ice shelfH includes one, two, or three layers, i.e., firn, meteoric ice, andmarine ice layers. Generally, meteoric and marine ice layers arelumped together as a single layer. Thus,

H = hf + hi; [S1]

where hi is the total thickness of meteoric ice layer and marineice layer and hf is the firn thickness.Although the actual thickness of the ice shelf is an important

geometry parameter, ice equivalent thickness, Hi, is used more

Liu et al. www.pnas.org/cgi/content/short/1415137112 2 of 10

often in mass calculations. The ice equivalent thickness refers tothe thickness of an ice shelf if all of the ice is at an average icedensity ρi (917 kg/m3), i.e., the reduced total thickness obtainedby compressing the variable-density firn layer until its densityequals that of ice,

Hi =�hf −Δh

�+ hi; [S2]

hfρf =�hf −Δh

�ρi; [S3]

where ρf is average density of the firn layer, and Δh is the FDC,defined as the difference between the combined ice/firn columnand the ice equivalent thickness.MCORDS thickness data have no firn correction (26), so the ice

equivalent thickness can be determined by removing an FDC fromthe MCORDS thickness.

Hi =�hf −Δh

�+ hi =

�hf + hi

�−Δh=H −Δh: [S4]

The ice equivalent thickness can be inferred from surface el-evation using the principle of hydrostatic equilibrium.

Hi =ðhasl −ΔhÞρw

ρw − ρi; [S5]

where hasl is ice shelf freeboard, i.e., the height difference be-tween ice shelf surface height and sea surface height, and ρw isthe density of the seawater column under the ice shelf. Seawaterdensity will vary with depth, so we want a representative densityat depths between the ice front (average 220 m) and the GL(average 710 m). Hence, we use 1,027 kg/m3 with an uncertaintyof 5 kg/m3 as suggested by ref. 27.We use ICESat GLAS data to obtain the ice shelf freeboard.

GLAS data preprocessing in ref. 13 is used in this study. Theelevation measured by satellite radar altimeter is referenced tothe WGS84 ellipsoid and should be first transformed to the el-evation relative to geoid. The local ocean surface is differentfrom global mean sea level resulting from nontidal effects. Themean dynamic topography (MDT) is defined as the height of themean ocean surface relative to the geoid. Ice shelf freeboard iscalculated as

hasl = ele− geoid−MDT; [S6]

where ele is the elevation referenced to the WGS84 ellipsoid,geoid is the geoid, and MDT is the local ocean mean dynamictopography. The EIGEN-6C2 gravitational model (22) is used tocalculate Antarctic geoid (icgem.gfz-potsdam.de/ICGEM/).The MDT near ice shelf fronts is calculated using ICESat

GLAS data coverage over the six different oceans (28) in summer(from February to April) of Antarctica.

MDT =

Pni=1

�eleseaðiÞ− geoidseaðiÞ

�n

; [S7]

where n is the number of points covering the specific oceans.More than a million GLAS points are used to calculate theMDTs in different ocean areas of Antarctica. The result showsthat the MDTs range from −1.08 m to −1.24 m.The FDC is used to account for the presence of a variable-

density layer. The firn layer makes up the majority of the ice shelfthickness uncertainty, and the FDC can dominate the errorbudget in the ice thickness estimates from surface elevation,assuming hydrostatic equilibrium (8, 27). It therefore complicatesan accurate assessment of the ice shelf mass balance, because the

greatest uncertainty arises in the calculation of the influx acrossthe GL and mass gain or loss from ice front advance and retreat.The FDC can be estimated by a firn densification model or by

combining the thickness and elevation measurements.We use recently updated Antarctic FDC from a recent firn

densification model (FDM) (29). The FDM was forced at thesurface by the surface mass balance, surface temperature, andnear-surface wind speed from a regional atmospheric climatemodel RACMO2/ANT, which was, in turn, forced at its lateralboundaries with a global atmospheric reanalysis from 1979,continuously updated in real time (ERA-Interim) reanalysisdata. Then, the FDC parameter was modeled from RACMO2/ANT model data available for the period 1979–2009 at a tem-poral resolution of 6 h and a spatial resolution of 27 km. Liquidwater processes (meltwater percolation, retention, and refreezing)are also included (29). However, the effect of heterogeneousinfiltration and refreezing has not been investigated at any level(e.g., ref. 30).Although the depth and density of the firn layer cannot be detected

by satellite, FDC can be calculated from the true thickness andfreeboard of the ice shelf by combining Eqs. S4 and S5.

Δh=ρwρi

hasl −ðρw − ρiÞ

ρiH: [S8]

Crossover points between MCORDS and GLAS tracks are usedto estimate the firn correction. Because of the limited number ofcrossover points, the results are only used to determine the mod-eled FDC uncertainty.TheRACMOmodel has limitations in estimating FDC because

of complex heterogeneous infiltration and refreezing for sit-uations where surface melt is significant (30). To weaken thislimitation, we correct the FDC in blue ice and melting areasusing a land cover map. The Antarctic land cover map was drawnby the College of Global Change and Earth System Science atBeijing Normal University. A classification system of Antarcticland cover was established with six categories and conducted bycombining computer-based and manual interpretation methodsbased on an improved Landsat Image Mosaic of Antarctica (31).It was produced with the combined use of 1,073 scenes ofLandsat-7 ETM+ obtained during 1999–2003 and MODIS dataacquired in 2005 covering from 82.5°S latitude to South Pole at90°. The areas of each category of blue ice, crevasse, ice-freerock, water body, moraine, and firn are: 225,207 km2 (1.65%),7,153 km2 (0.05%), 72,958 km2 (0.535%), 189 km2 (0.001%), 310km2 (0.003%), and 13,337,393 km2 (97.7%), respectively. This landcover map was used to correct values of FDC to 0 for areas ofblue ice and water body in this paper. In individual thicknesscalculation, the FDC of the GLAS or MCORDS measurementlocations within 1 km of blue ice or melt pond is set to zero.

GL thicknesses. The GL positions come from combinedMEaSUREs (20) and ASAID GL (21), just as it is used in de-lineation of ice shelf extent. The GL location precision is veryimportant, because inferred grounded ice thickness may beerroneously high if we incorrectly assume hydrostatic equilibrium.Most GL positions use the MEaSUREs GL, which is thought tobe more systematic and precise (8, 10). To minimize the risk ofincluding the measurements of grounded ice and ice shelf ice faraway from the GL, only the measurements within a distance of900 m from the GL are used. First, the vector GL map is con-verted to raster GL at 900 m resolution, which is equal to the pixelsize of the velocity data, and then converted to point vector GLs.Second, the GL points with measurements within a distance of450 m are selected. Measurements of a GL thickness that fallbeyond 3 SDs are excluded, and the mean of the rest is taken asthe thickness of this GL point. Then, the remaining GL pointswith measurements within a distance of 450 m are selected.

Liu et al. www.pnas.org/cgi/content/short/1415137112 3 of 10

Their thicknesses are determined as above. Finally, the thicknessof the other GL points is determined from these points throughthe shortest-distance principle.

Subbasin average thickness of ice front change area. Considering thelow-density distribution of both GLAS points and MCORDSpoints in the change areas (including advance, retreat, and icebergcalving) at the ice front, we use the mean value of all individualmeasurements covering the ice front change area (excluding themeasurements that fall beyond 3 SDs) in a subbasin system as thethickness in mass estimation of advance, retreat, and icebergcalving in this subbasin system (Dataset S1).Ice flow velocity. We use MEaSUREs Interferometry SyntheticAperture Radar (InSAR)-based velocity data (19) at a resolutionof 900 m for the period 2007–2008 derived from six sensors(available at nsidc.org/data/docs/measures/nsidc0484_rignot). Thetotal error (the square root of the sum of the independent errorssquared) of MEaSUREs velocity ranges from 1 m/y to greaterthan 17 m/y (the average is 4 m/y), and average direction error is1.7° (8). MEaSUREs velocity is used in flow-line tracking (Antarcticsurface flow-line mapping) and GL flux calculation (Cross-GL fluxes).Ice shelf advance or retreat.We obtained Antarctic ice shelf extentsin August 2005 and August 2011 from ASAR mosaic imagescombined with the GL and island area. The advance or retreatarea is calculated by spatial analysis using ArcGIS software. Thechange in the GL position is not included in this analysis. The twoperiod data have a good spatial and temporal consistency. Thegeolocation accuracy between the two mosaic images is less thanone pixel (75m). Themean annual advance or retreat in 6 y insteadof annual change is used to decrease the area detection error.Fig. 2 shows ice shelf advance or retreat between 2005 and 2011.Ice shelf thickening or thinning. The mass gain or loss from ice shelfthickening or thinning is calculated by the area of floating parts andits average thickness change. We use the previous results of averageice shelf thickness change ∂H=∂t in ref. 13 derived using IceSat-1GLAS data for the period 2003–2008 [available at www.nature.com/nature/journal/v484/n7395/full/nature10968.html#supplementary-information (Supplementary Table 1)]. There are some small iceshelves with no estimates. For these ice shelves, we use the mea-surements from adjacent shelves.Cross-GL fluxes. Ice flux across the GL is determined using a newflow-line routing algorithm. To obtain detailed ice fluxes, the GLis divided into many small segments with identical length. A fluxgate calculation is made for each line segment. The ice flux FGiacross a line segment is calculated as

FGi =HiViLiρi; [S9]

where Vi is magnitude of flow velocity, Hi is ice thickness, andthe across-flow width of the flux gate, Li, is calculated as

Li =ΔL× sinðαÞ; [S10]

where α is the angle between the ice flow direction and the linesegment and ΔL is the pixel size of the velocity raster data (900 m).A very important step in ice flux estimation is determining the

overlap of the along-flow flux gates, which is likely to overestimateice flux due to deviations of theGL. Based on flow-line routes, theoverlap of the flux gates along the ice flow is considered andprocessed (Fig. S3). First, we track flow lines from the GL pixels(pixel size 900 m, same as the velocity raster data) that the middlepoints of the GL line segments fall in. Then we transform thevector flow-line map into a raster flow-line map with the samespatial resolution as the velocity data. The value of pixels coveredby flow lines downstream of the GL is set to 1, and all other pixelsare set to 0. We determine the overlap GL pixels. If every value ofthe four connected pixels of a GL pixel is 1, it is determined as anoverlap GL pixel. Finally, redo steps 1 and 2 using the GL pixelswithout the overlaps at step 3 to examine whether there are

obvious missing pixels along a flow line in the new raster flow-line map compared with the one tracked from the original GLpixels. If there are, the pseudo-overlap GL pixels are detectedand recovered. All of the GL line segments whose middle pointsfall in the true overlap GL pixel are determined as the overlapflux gates, which are excluded from the ice flux calculation.SMB.The SMB (or surface accumulation and melt) are derived fromthe regional atmospheric climate model RACMO2/ANT for theperiod 1979–2009 at a temporal resolution of 6 h and a spatialresolution of 27 km (29) (provided by M. R. van den Broeke).However, considering the consistence of temporal scale, the

firn height change we used in this paper is derived from a firnmodel UUFIRNMODELv3.1/ANT forced by climate data fromRACMOv3.2/ANT27 for the period 2003–2008 (13) (available atdoi.pangaea.de/10.1594/PANGAEA.775983). They run for 99sites on Antarctic ice shelves. Surface accumulation, melt, andmass balance of 99 sites were interpolated to all ice shelves usingthe shortest-distance principle. The volume mass is processed at27-km spacing.Iceberg calving. Iceberg calving detection is more than ice frontchange detection, because the ice front keeps flowing, i.e., icefront advance and iceberg calving occur at the same time. Wedetected the location of calving events, delineated the ice front,and then detected the calving area by ice front registration usingthe features on the ice shelf before and after calving (Fig. S4).

Calving events detection. Traversing Antarctic coastline andcomparing with the ASAR WSM image mosaic in August ofthe current year (the original image) and the following year (thesecond image), calving events are detected according to thechanges at the front of ice shelves. The ice shelf front is likely tocalve when extending forward; if advance and retreat are equal,there may be no obvious change occurring to the ice shelf front.To avoid misjudgment caused by this, the ice front movements areestimated by flow-line methods. Thus, even if there is neitheradvance nor retreat occurring at the front of an ice shelf, calvingcould be detected. The calved area is an enclosed polygon betweenthe outer boundary (ice shelf ice front) and the inner boundary(fracture line) over a year. The calved areas are manually detectedby using coregistered pairs of consecutive August 2005, 2006,2007, 2008, 2009, 2010, and 2011 Envisat ASAR image mosaics.

Recurrence interval. Recurrence interval is defined as the timebetween the two major calving events at the same calving front.Calving recurrence means that two calving events occur in thesame spatial neighborhood and their areas are the same order ofmagnitude. In this paper, RADARSAT-1 mosaic images of 1997and ASAR images from 2005 to 2011 can be used to determinerecurrence frequency of calving events. Individual calved areasbetween 1997 and 2005 and calving events between 2005 and 2011are first determined. If one calving event in this year is spatiallyadjacent to other calving events in another year between 2005 and2011 and their calved areas are of the same order of magnitude,their recurrence interval is less than 7 y. If the remaining isolatedcalving events have the same spatial neighborhood with calvedarea between 1997 and 2011 and of the same size magnitude, theirrecurrence intervals is less than 14 y. The infrequent tabulariceberg calving process is marked by several decades of quies-cence between major calving events. Thus, the recurrent calvingevents in our observation period of 1997–2011 can be seen asfrequent calving events.Iceberg calving C is calculated by annual cumulative calving

area AC and its mean subbasin ice thicknesses at ice front HC(Ice thicknesses).

C=ACHCρi: [S11]Basal melt.The basal melt or freezing is estimated at subbasin scalefrom the results of ice shelf mass balance, estimated from ice shelfthickness and extent change, ice flux at GL, SMB, and iceberg

Liu et al. www.pnas.org/cgi/content/short/1415137112 4 of 10

calving. These data do not have exact time consistency. Iceshelf net thickening and SMB are averages for the period 2003–2008, ice flux is the average for 2007–2008, and iceberg calvingis the average for 2005–2011. Thus, we see basal melt calcu-lated in this study as an estimate for the average for period2003–2011. The basal melt in 2003–2011 is given both in massper year (gigatonnes per year) and in ice equivalent thickness(assuming a density of 917 kg/m3) per year (meters per year)(Dataset S1).

Uncertainty Estimation. The uncertainty assessment is done sepa-rately for each subbasin. We assume the subbasins have depen-dencies in a sector but the sectors are independent of each other.The uncertainty estimation follows the rules of error propagation.Density uncertainties. The uncertainties of both ρi and ρw are around5 kg/m3 (27).Area uncertainties. Area error is smaller than other errors. The un-certainty is determined by the geolocation accuracy of the GL(100 m) (10) and delineated boundary at ice shelf front or boundaryof calving area. The standard uncertainty of area is given as

uA = 0:05× l; [S12]

where l is the perimeter (kilometers) of the area A (square kilo-meters). Eq. S12 is justified based on the comparison betweenthe same area delineated from ASAR image at 75-m spacing andthat from RADARSAT image at 25-m spacing.Thickness uncertainties.

Uncertainty of individual MCORDS thickness. Uncertainty of in-dividual MCORDS thickness includes systematical and randomstandard uncertainty uHs, uHr ,

uH =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2Hs + u2Hr

q: [S13]

The systematical error mainly comes from instruments. Thedata are not radiometrically calibrated. The primary error of icepenetrating radar data consists of system electronic noise, mul-tiple reflectors, and off-nadir reflections. No compensation wasdone for a firn layer by MCORDS SAR processing where the iceis treated as a homogeneous medium with a dielectric of 3.15 andthe dielectric error is expected to be on the order of 1% for typicaldry ice (26). The dielectric error is given by

uHr =H2«%error = 0:005×H: [S14]

Crossover analysis is used for the estimate of MCORDS icethickness random error. For MCORDS L2 Ice Thickness, thecrossover errors measurements are available from the 2009Operation IceBridge campaign, and are provided by the Centerfor Remote Sensing of Ice Sheets (CReSIS). They are the onlyreliable estimate of thickness measurement errors available, butthese crossover errors have not yet covered all of the Antarcticcampaigns or data covering areas. The MCORDS L2 IceThickness data sets of Antarctic campaigns from 2009 to 2011 areused in this study. The CReSIS’s crossover error analysis methodis used here. The process is as follows. (i) Calculate crossoverpoints and difference distribution. (ii) Discard extreme values inlocations where thickness is 0 or very small, and the terrain hasdramatic ups and downs, such as in mountainous areas. First, onlythickness data with high quality of 1 (high confidence pick) arechosen. Second, for the areas where thickness is larger than 4 m, thetriple standard difference method (3-δ principle) is used repeatedlyto filter these extreme values until the change of SD is less than 1 m.(iii) Determine measurement error (error estimation).The result of uHr is 23.6 m, which is estimated from 14,322

crossover points, thus,

uHi IB =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi23:62 + ð0:005×HÞ2

q: [S15]

Uncertainty of estimated FDC. The uncertainty of individual esti-mated FDC from MCORDS thickness and GLAS freeboard iscalculated as

uΔh =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ρwρi

�2

u2hasl +�ρw − ρi

ρi

�2

u2H

s; [S16]

where uhasl is uncertainty of GLAS freeboard, as discussed inEq. S21.The modeled FDC have a good agreement with the ice core

measurements data (29), but the in situ measurements are lim-ited. There is no available error estimation of modeled FDC. Weused 105 grids of modeled FDC, each of which contains morethan 30 estimated FDC points (more than 3,150 crossover pointsbetween GLAS and MCORDS), to estimate the uncertainty ofthe modeled FDC. The standard uncertainty of the average es-timated FDC of a grid is calculated as

uΔhge =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2Δh + σ2Δhge

n

s; [S17]

where Δhge is the average estimated FDC of a grid, Δh is anindividual estimated FDC, and n is the number of samples ina grid. The mean of the individual standard uncertainty of thegrid average estimated FDC is 0.57 m, ranging from 0.286 m to1.17 m.If the estimated grid average FDC is thought of as true

value, the standard uncertainty of modeled FDC is calculatedas follows.

uΔhgm =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni=1

�Δhgm −Δhge

�2N − 1

s; [S18]

where Δhgm is the individual modeled FDC, and N is the numberof sample grids; 105 sample grids are used to estimate the standarduncertainty. The result showed that the standard uncertainty is3.04 m. If we use a linear LSE to correct the modeled FDC, thestandard uncertainty of the corrected modeled FDC is 2.88 m. Infact, the estimated grid average FDC also has its errors.

Uncertainty of individual equivalent thickness estimated from MCORDSthickness. The uncertainty of individual MCORDS equivalentthickness is determined by uncertainties of MCORDS thicknessuH and FDC uΔh. The combined standard uncertainty of an in-dividual estimation is given as

uHi IB =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2H + u2Δh

q=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi23:72 + ð0:005×HÞ2

q: [S19]

The result showed that the MCORDS ice equivalent thicknesserror is dominated by MCORDS thickness measurement.

Uncertainty of individual equivalent thickness estimated from GLASthickness. Crossover analysis between GLAS and MCORDSthicknesses is also used to estimate the uncertainty of GLAS icethickness. The uncertainty of GLAS thickness estimated is 29.3 mfrom 623 crossover point pairs.The uncertainty of GLAS ice thickness is also estimated from

uncertainties of estimated freeboard uhasl and modeled FDC uΔh.Ignoring the uncertainty of density of ρw and ρi, the uncertainty

of GLAS ice thickness can be estimated as

Liu et al. www.pnas.org/cgi/content/short/1415137112 5 of 10

uHi GS =ρw

ρw−ρice

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2hasl + u2Δh

q: [S20]

The uncertainty of ice shelf freeboard is mainly caused byGLAS elevation measurement, the geoid correction, and the localmean dynamic topography correction. MDT is calculated fromelesea and geoidsea in the local ocean near ice shelf fronts, so itprobably has little correlation with ele and geoid of the ice shelf.The three error parts are likely to be independent of each other.The combined standard uncertainty of ice shelf freeboard mea-surement can be represented as

uhasl =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2ele + u2geoid + u2MDT

q; [S21]

where uele, ugeoid, and uMDT are standard uncertainty of ele,geoid, and MDT, respectively.The GLAS single-shot error sources for elevation measure-

ments are mainly from precision orbit determination, precisionattitude determination, and atmospheric delay (16). Additionalerror sources arise on the ice shelves from the tide model theinverse barometer correction and variation from mean dynamictopography. The combined individual elevation uncertainty isestimated as 0.147 m.The comparison of geoid heights derived from the EIGEN-6C2

model with GPS/leveling derived geoid values fromUnited States,Canada, Europe, Australia, and Japan [Spectral Comparison withthe Model EIGEN-6C2 (icdc.zmaw.de/geoid_eigen.html?&L=1)].It gave a root-mean-square difference of up to 0.249 m and a totalerror budget of 0.216 m. There is no direct comparison fromAntarctica, and we gave Antarctic EIGEN 6C-2 geoid standarduncertainty of 0.249 m.The standard uncertainty contributions of mean dynamic to-

pography are from GLAS elevation measurement, geoid mea-surement, and its spatial variation. The spatial averaging over theseven ocean areas near Antarctic coast employs between 148,000and 400,000 points. The uncertainty in individual elevationmeasurements along an ICESat pass is thought to be correlated,but elevation measurements between ICESat passes are probablyindependent (13). We assumed the geoid uncertainty is spatiallyindependent. The combined uncertainty of averaged mean dy-namic topography can be calculated as

uMDT =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2ele

�1

npasses−

1npoints

�+u2geoidnpoints

+σ2MDT

npoints

s; [S22]

where σMDT is the SD of averaged mean dynamic topography andnpoints and npasses are the number of elevation measurements andthe number of unique combinations of ICESat passes, respec-tively. The combined standard uncertainty uMDT is up to 0.008 m.Combining these three uncertainties gives an individual un-

certainty of ice shelf freeboard of 0.289 m as follows.

uhasl =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2Xele

+ u2Xgeoid

+ u2hseaq

= 0:289: [S23]

Thus, combining the uncertainties of freeboard and FDC givesan individual uncertainty of GLAS ice thickness as follows.

uHi GS =1;027

1;027− 917

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:2892 + 2:422

p= 23:4: [S24]

The uncertainty of subbasin average ice thickness of change and calvingarea at ice shelf front uH. Considering the low density of both GLASpoints and MCORDS points in the changed area at the ice front,

we take the subbasin average ice thickness as the ice thickness ofthe changed area. Since the measurement errors of MCORDSice thickness and GLAS ice thickness are in a similar range,both MCORDS and GLAS are used in this estimation. Thus,

uH =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffinIGn

u2Hi IS+nGS

nu2Hi GS

+σH2

n

s[S25]

where nIG, nGS, and n are the number of MCORDS, GLAS,and total measurements used; σH is the SD of the total thicknessmeasurements.

The uncertainty of ice thickness at the GL uHi MO . The ice thicknessesof uniform discrete units of 900 m in size at the GL are directlyor indirectly determined by MCORDS ice thickness and GLASice thickness. The units with no GLAS or MCORDS thicknessesare interpolated by those nearby. The uncertainty of ice thicknessuHi MO is given as

uHi =

8<:

uHi IB

uHi GS

uHi MO

: [S26]

The error of interpolated ice thicknesses is given as 100 m (10).

uHi MO = 100: [S27]

Thickness change uncertainties.Uncertainty estimation of uΔH. The data of ΔH estimated from

GLAS elevation change are from Pritchard et al. (13), and theiroverall combined uncertainty uΔH is dominated by the uncertaintyin the FDC. We derived the uncertainty estimation of uΔH fromtheir elevation change Δhele uncertainty estimation uΔhele ,

uΔHΔT=

1;0271;027− 917

× uΔheleΔT

: [S28]

The data are nearly ice shelf independent, and the uncertaintyranged from 0.03 to ∼0.50 m. There are still missing data in someareas where we used the proximity principle to estimate ΔH, andgave them the maximum error of 0.50 m.

Uncertainty estimation of uΔHAccu , uΔHMelt . The values of ΔHMelt andΔHAccu are estimated by combining the results of the firnmodel UUFIRNMODELv3.1/ANT forced by climate data fromRACMOv3.2/ANT27 and elevation change obtained from ICESATGLAS data from 2003 to 2008. An estimated uncertainty in thelong-term accumulation trend of 8% is based on the strongrelationship between accumulation and temperature found inRACMO2, whereas an uncertainty in RACMO2 surface meltrate at 20% is estimated by comparing with observed melt ratesat two sites (13).The data are nearly ice shelf independent. The ArcGIS

shapefile of ice shelf extent are transformed onto a 27 km × 27 kmgrid cell. The cell accumulation and melt are obtained from theoriginal point data by using the proximity principle. The long-term annual average accumulation and melt products of thefirn model UUFIRNMODELv3.1/ANT are used in the missingdata areas. Because the accumulation is much larger than surfacemelt, the uncertainties of SMB are dominated by the uncertaintiesof mean annual accumulation.

Velocity Uncertainty at the GL. The total velocity error (the squareroot of the sum of the independent errors squared) of Antarcticaranges from 1 m/y to greater than 17 m/y. We take the averageuncertainty of velocity at the GL to be 4 m/y (8).

Liu et al. www.pnas.org/cgi/content/short/1415137112 6 of 10

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Fig. S1. Spatial distribution of Antarctic calving events in different calving styles and calving scales from 2005 to 2011. Four calving scales are divided: small(1∼10 km2), medium (10∼100 km2), large (100∼1,000 km2) and extra-large (larger than 1,000 km2).

Liu et al. www.pnas.org/cgi/content/short/1415137112 7 of 10

Fig. S2. Antarctic flow-line map. Different colors identify different basin flow systems.

Fig. S3. Flux gate filtering. The background image is MOA. (A) Tracking flow lines from GLs: The yellow line marks the GLs, the black boxes are the GL pixels,and the gray lines are flow lines tracking from the GL pixels. (B) Determining overlapping GL pixels: The red pixels are flow lines covering pixels and the greenboxes are overlapping GL pixels along the flow. (C) Examining mistakenly deleted GL pixels: The red pixels are flow line covering pixels excluding the over-lapping GL pixels in B and blue boxes are pseudo-overlapping GL pixels.

Liu et al. www.pnas.org/cgi/content/short/1415137112 8 of 10

Fig. S4. Sketch map of calving area detection on ASAR WSM images: (A and B) ice front lineated from ASAR images; (C) ice front registration by featuretracking; and (D) the ice front spatially shifted according to ice front registration and calving areas detected.

Table S1. Comparison of the ice front flux calculated in thisstudy (averaged over 2005–2011) and Rignot et al. (8) (averagedover 2007–2008)

Sector This study, Gt/y Rignot, Gt/y

Antarctica 1025 ± 39 1089 ± 139Filchner-Ronne 212 ± 17 221 ± 26East Antarctica KB 119 ± 17 130 ± 22Amery 35 ± 2 50 ± 8East Antarctica CE 270 ± 15 236 ± 33Ross 148 ± 6 146 ± 12West Antarctica 197 ± 17 225 ± 17Peninsula 44 ± 19 69 ± 13

Table S2. Area mean melt rate (meter ice equivalent per year, assuming density is 917 kg/m3) ofthe larger Antarctic ice shelves

Locations This study Glaciological estimate FESOM BRIOS

Antarctica 1.07 1.05 1.16 0.80Sum of ten 0.50 0.58 0.98 0.79Filchner-Ronne 0.02 0.38 0.34 0.32Brunt + Riiser-Larsen 0.27 0.13 0.92 3.38Fimbulisen +Jelbart 0.77 0.40 2.80 4.91Larsen C 1.04 0.49 1.00 0.60George VI 4.02 4.14 3.60 0.43Abbot 1.17 1.90 3.10 0.60Pine Island 14.00 17.66 3.10 —

Getz 4.82 4.65 5.40 1.95Ross 0.06 0.10 0.60 0.49Amery 1.66 0.64 2.90 0.35

This study is averaged over 2003–2011. Glaciological estimate averaged over 2007–2008 (8), FESOM averagedover 1980–1999 (11), and BRIOS 2004 (12). “Sum of ten” refers to the 10 largest ice shelves alone. —, no data.

Liu et al. www.pnas.org/cgi/content/short/1415137112 9 of 10

Table S3. The spatial distribution of total calving events of the infrequent tabular calving andfrequent disintegration calving in seven sectors (see Dataset S1) from 2005 to 2011

Sector

Number of calving events

Infrequent tabular calving Frequent disintegration calving All

Antarctica 152 427 579Filchner-Ronne 0 0 0East Antarctica KB 41 28 69Amery 1 0 1East Antarctica CE 45 177 222Ross 5 0 5West Antarctica 39 142 181Peninsula 21 80 101

Table S4. Mean percentage of calving events, area, and mass loss for four different spatial scales from 2005 to 2011

Scale category

Frequency, % Calving area, % Mass loss, %

Annual mean Range Annual mean Range Annual mean Range

Small (<10 km2) 60.3 ± 0.1 [56.6,65.4] 5.9 ± 0.2 [3.5,13.4] 6.8 ± 0.1 [3.3,13.1]Medium (10−100 km2) 34.7 ± 0.3 [28.3,40.8] 26.5 ± 8.2 [9.2,79.7] 31.4 ± 7.8 [7.5,80]Large (100−1,000 km2) 4.5 ± 0 [1,7.2] 25.7 ± 7.6 [6.9,71.7] 24.5 ± 6.7 [4.5,68.1]Extralarge (>1,000 km2) 0.5 ± 0 [0,2.3] 41.8 ± 16.9 [0,78.1] 37.2 ± 15.9 [0,84.8]

Other Supporting Information Files

Dataset S1 (XLS)

Liu et al. www.pnas.org/cgi/content/short/1415137112 10 of 10